WASHINGTON—President Donald Trump signaled for a second straight day his frustration with the Federal Reserve’s policy of gradually raising interest rates, saying it would undermine his campaign to boost U.S. economic growth and reduce trade deficits.

In tweets on Friday, Mr. Trump said the Fed’s efforts hurt the U.S. economic expansion, and he accused China and Europe of manipulating their currencies to hurt the U.S. on trade.

The central bank’s campaign to slowly raise interest rates “hurts all that we have done,” he wrote Friday. “The U.S. should be allowed to recapture what was lost due to illegal currency manipulation and BAD Trade Deals. Debt coming due & we are raising rates — Really?”

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In effect, Mr. Trump signaled his desire to enlist the Fed in his broader trade campaign. Higher interest rates in the U.S. could raise the value of the U.S. dollar against other currencies, which would make it harder to narrow the trade deficit. A stronger greenback makes U.S. exports relatively more expensive on world markets. Mr. Trump regards the trade deficit as an important scorecard of economic vitality, though most economists say it isn’t.

A spokeswoman for the Fed’s board in Washington declined to comment.

The central bank is unlikely to yield to such pressure. Since the 1980s, the Fed has vigorously defended its mandate to maximize employment and seek stable prices, which in recent years it has formalized by aiming to keep inflation around 2%, a level consistent with healthy economic growth.

Monetary policy isn’t the only reason the dollar has strengthened this year. Mr. Trump’s own policies—including the tax cut the president signed into law last December and the federal spending increase he approved in February—have also contributed to stronger economic growth and higher budget deficits, which put upward pressure on the U.S. currency.

Recent currency strength could be exacerbated because the Fed is ahead of other global central banks in lifting interest rates after nearly a decade of efforts to stimulate growth by keeping rates at ultralow levels.

Europe is “making money easy, and their currency is falling,” Mr. Trump told CNBC Thursday. “China, their currency is dropping like a rock. Our currency is going up.”

The euro is down 5.3% versus the dollar since early February, while the yuan is down 7.5% against the dollar from its recent high, also in early February.

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Should Mr. Trump follow through with imposing tariffs on more goods, such as European cars, any potential shocks could encourage monetary policy authorities abroad to keep interest rates lower than they might otherwise be.

With the U.S. economy expanding solidly, unemployment low and inflation around 2%, the Fed is closer than it has been in more than a decade to achieving its goals. Mr. Trump’s fiscal policies, which are projected to stimulate growth this year and next, have also given the Fed greater conviction to continue with rate increases.

A Trump administration official said Friday the White House was comfortable with the Fed’s plans but hoped the central bank would only raise rates once more this year.

Central banks and bond investors have argued that an independent central bank is important to guard against inflation, after political interference in the 1960s and 1970s was widely blamed for contributing to runaway inflation.

After Mr. Trump’s initial comments about the Fed ricocheted through currency and bond markets on Thursday, the White House sought to clarify them by saying he still respected the Fed’s independence.

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An administration official said Friday that Mr. Trump was expressing in public what he has said in private for some time and that the president was neither trying to interfere with the Fed nor escalate his attacks.

Still, the official acknowledged the possibility that such an escalation could happen later because it was difficult to predict what Mr. Trump might do.

The president has been silent about Fed policy until now, in keeping with a tradition that stretches back through at least three administrations of both parties of refraining from commenting on central bank decisions in respect for its independence.

“The president has a certain style. He wants to get in on all these debates,” said St. Louis Fed President James Bullard, following a speech in Glasgow, Ky., on Friday. “He’s going to weigh in…. He’ll probably weigh in lots in the future. Different presidents have different styles. That’s the way it is.”

Mr. Bullard said the bigger threat to the Fed would be if Congress were to amend legislation that changes the governance structure of the central bank. “The structure is already designed to put a big committee together and try to get a lot of analysis behind these decisions,” he said.

Fed Chairman Jerome Powell was in Argentina on Friday for the Group of 20 summit of finance ministers, which Treasury Secretary Steven Mnuchin is also set to attend.

Mr. Powell said last week he wasn’t worried about political pressure from the White House. “We do our work in a strictly nonpolitical way, based on detailed analysis, which we put on the record transparently,” Mr. Powell said in an interview with American Public Media’s “Marketplace” radio program.

Mr. Trump has repeatedly referred to himself as a “low-interest rate person,” reflecting in part his career in real estate. Few industries have benefited as much from the Fed’s campaign over the past decade to stimulate growth as the real-estate industry.

Mr. Trump’s new economic adviser, Lawrence Kudlow, has in the past warned against political officials pushing the Fed too far. “Republicans attacking [Fed Chairwoman Janet] Yellen…should be careful what they wish for,” he wrote in a CNBC commentary in 2015.

In the same article, Mr. Kudlow highlighted the economic troubles that followed President Richard Nixon’s efforts to influence the Fed. “The Fed has a point about politics,” he wrote.